Effects of structural uncertainties on TMD design: A reliability‐based approach

This study investigates the effects of structural uncertainties on the design and performance evaluation of passive tuned mass dampers (TMD) used for vibration control. A probabilistic optimal design methodology is presented in which time‐invariant uncertain structural parameters are modelled by random variables with prescribed probability distribution. Unlike conventional TMD designs based on minimizing the mean‐square response, a reliability‐based performance index is considered in the proposed design which properly accounts for uncertainties in load and structural models. An approximate asymptotic expansion is used to compute the multidimensional reliability integrals arising in the proposed optimal design methodology. Accuracy and effectiveness issues are addressed by comparing results obtained using this approximation with corresponding results obtained by numerical integration. The importance of structural uncertainties is demonstrated by applying the methodology to a single degree of freedom structure subjected to broadband excitations that are modelled by stationary white noise. It is found that the consideration of structural uncertainties improves substantially the robustness of the TMD design. Also, the reliability‐based TMD‐design methodology results into significantly larger structural reliability compared to that obtained by the conventional design approach based on minimizing the mean‐square response.